Numeracy and Decision Making

Author(s): Ellen Peters, Daniel Västfjäll, Paul Slovic, C. K. Mertz, Ketti Mazzocco and

Stephan Dickert

Source: Psychological Science, Vol. 17, No. 5 (May, 2006), pp. 407-413

Published by: Sage Publications, Inc. on behalf of the Association for Psychological Science

Stable URL: http://www.jstor.org/stable/40064557

Accessed: 08-06-2017 18:28 UTC

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Numeracy and Decision Making Ellen Peters,1'2 Daniel Vastfjall,1'3 Paul Slovic,1'2 C.K. Mertz,1 Ketti Mazzocco,4 and Stephan Dickert1'2

PSYCHOLOGICAL SCIENCE

Research Article

Decision Research, Eugene, Oregon; University of Oregon; Goteborg University, Goteborg, Sweden; and University

ofTrento, Trento, Italy

ABSTRACT- A series of four studies explored how the ability to comprehend and transform probability numbers relates to performance on judgment and decision tasks. On the surface, the tasks in the four studies appear to be widely different; at a conceptual level, however, they all involve processing numbers and the potential to show an influence of affect. Findings were consistent with highly numerate individuals being more likely to retrieve and use appro- priate numerical principles, thus making themselves less susceptible to framing effects, compared with less numer- ate individuals. In addition, the highly numerate tended to draw different (generally stronger or more precise) affective meaning from numbers and numerical compari- sons, and their affective responses were more precise. Al- though generally helpful, this tendency may sometimes lead to worse decisions. The less numerate were influenced more by competing, irrelevant affective considerations. Analyses showed that the effect of numeracy was not due to general intelligence. Numerical ability appears to matter to judgments and decisions in important ways.

Although many judgments and decisions rely heavily on un- derstanding basic mathematical concepts, little research has examined the role of numerical ability, or numeracy, in decision

tasks. Numeracy is defined as the ability to process basic probability and numerical concepts. Making good decisions in the real world requires some numerical ability. For example, Hamm, Bard, and Scheid (2003) found that greater numeracy was associated with more accuracy in making judgments about

probabilities associated with prostate cancer screening. Gur- mankin, Baron, and Armstrong (2004) found that less numerate individuals trusted verbal risk information more than numeric

risk information from physicians, whereas more numerate in-

dividuals showed the opposite effect. Paulos (1988) argued that the inability to deal "rationally" with small likelihoods of large

outcomes (e.g., a highly unlikely but catastrophic outbreak of a

disease) results in misinformed government policies, confused

personal decisions, and an increased susceptibility to pseudo- science. Recent research in numeracy (e.g., Lipkus, Samsa, & Rimer, 2001; Woloshin, Schwartz, Black, & Welch, 1999) sug- gests that people differ substantially in numerical ability and that many people are "innumerate" (Paulos, 1988). Data from the National Literacy Survey indicate that about half of Amer- icans lack the minimal mathematical skills needed to use

numbers embedded in printed materials (Kirsch, Jungeblut, Jenkins, & Kolstad, 2002). In today's increasingly technical world, innumeracy may be a critical obstacle to making good decisions in financial, medical, and other domains.

One goal of the present research was to relate numeracy to

performance on decision problems that appear to rely on par- ticipants' ability to retrieve and use appropriate numerical principles. We suggest that some of the best-known effects in

judgment and decision research, such as framing effects, may result particularly from those participants who are least likely to

apply these numerical principles.

Studies 1 and 2 examined the hypothesis that the framing of

numerical information has greater effects on the less numerate

than the highly numerate. Studies 3 and 4 introduce the idea that

numeracy influences affect and the clarity of affect toward nu-

merical information in ways that matter to decision making.

STUDY 1: NUMERACY AND ATTRIBUTE FRAMING

Results of framing studies suggest that information providers (e.g., physicians, advisors, con artists) can influence decisions without distorting information, merely by how they frame out-

comes. In Study 1, we focused on attribute framing (Levin, Schneider, & Gaeth, 1998), in which a single attribute is the subject of framing. Levin and Gaeth (1988), for example, found

that perceptions of the quality of ground beef depended on whether the beef was labeled as "75% lean" or "25% fat" (the beef was rated as better tasting and less greasy when given the

former label). Previous research has examined whether math skill is related

to framing effects. For example, Stanovich and West (1998) found that decision makers with higher SAT scores were less likely to show a within-subjects effect of presenting risky choices in positive versus negative frames (e.g., the number of

Address correspondence to Ellen Peters, Decision Research, 1201 Oak St., Suite 200, Eugene, OR 97401, e-mail: empeters@uoregon.edu.

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Numeracy and Decision Making

TABLE 1

The 11 Items in the Numeracy Scale Developed by Lipkus, Samsa, and Rimer (2001) and Used in All Four Studies

Percentage Item correct in Study 1

4. Which of the following numbers represents the biggest risk of getting a disease? 1 in 100, 1 in 1000, 1 in 10 96 5. Which of the following represents the biggest risk of getting a disease? 1%, 10%, 5% 94

8A. If the chance of getting a disease is 10%, how many people would be expected to get the disease out of 100? 90 8B. If the chance of getting a disease is 10%, how many people would be expected to get the disease out of 1000? 84 9. If the chance of getting a disease is 20 out of 100, this would be the same as having a

chance of getting the disease. 6. If Person A's risk of getting a disease is 1% in ten years, and Person B's risk is double that of A's, what is B's risk? 83 7. If Person A's chance of getting a disease is 1 in 100 in ten years, and Person B's risk is double that of A, what is B's risk? 74 2. In the BIG BUCKS LOTTERY, the chances of winning a $10.00 prize are 1%. What is your best guess about how 69 many people would win a $10.00 prize if 1,000 people each buy a single ticket from BIG BUCKS?

1. Imagine that we roll a fair, six-sided die 1,000 times. Out of 1,000 rolls, how many times do you think the die would 61 come up even (2, 4, or 6)?

10. The chance of getting a viral infection is .0005. Out of 10,000 people, about how many of them are 56 expected to get infected?

3. In the ACME PUBLISHING SWEEPSTAKES, the chance of winning a car is 1 in 1,000. What percent of tickets of 46 ACME PUBLISHING SWEEPSTAKES win a car?

Note. In Study 1, the mean score was 8.4, and the median was 9.

lives saved vs. the equivalent number of lives lost). Simon, Fagley, and Halleran (2004) found that among individuals high in need for cognition, those who rated their math skills as high

were not influenced as much by the framing of risky choices as were those who rated their skills as low. To the best of our

knowledge, no studies have examined the effects of actual number performance on the influence of frames, and especially attribute frames.

Method

Participants (TV = 100, 45% female, mean age = 26) were recruited using a campus newspaper and were paid $10. Our measure of numeracy was the total number of correct responses

to 11 items testing comprehension of probabilistic information

(see Table 1). Framing effects were tested by presenting par- ticipants with the exam scores of five psychology students and

asking them to rate each student's quality of work on a 7-point

scale ranging from -3 (very poor) to +3 (very good). The framing

of exam scores was manipulated between subjects; the scores were presented in terms of either the percentage correct or the

percentage incorrect, so that "Emily," for example, was de- scribed as receiving either 74% correct or 26% incorrect on her

exam. We predicted that the difference in ratings between the

positive- and negative-frame conditions would be greatest among the least numerate individuals.

This study was administered as part of a series of paper-and-

pencil experiments, with the numeracy measure and demo- graphic items presented last. This same order (decision tasks, numeracy measure, and demographic items) was used for all the

studies reported in this article.

Results

The mean numeracy score was 8.4 (median = 9) out of 11 possible (range = 2-11; a = .68). Because the distribution was highly skewed, we performed a median split on the measure. Note that the results for the numeracy measure were similar in

Studies 2 through 4, and we used a median split for analyses in those studies as well (sample sizes were small in two of our

studies, making quartile and other splits less viable). Thus, our

analyses compared the participants who were most numerate (9,

10, or 11 correct) with those who were less numerate (2-8 items

correct). Although we recognize that dichotomous splits are associated with problems such as loss of power, the skewness in

the variable justifies our choice (MacCallum, Zhang, Preacher, & Rucker, 2002). Results with quartile splits of numeracy were

similar to those with median splits in Studies 1 and 4, which had

the largest sample sizes. In a repeated measures analysis of variance (ANOVA) of the

performance ratings, the usual framing effect was found. The

more positive frame elicited more positive ratings: Mean per- formance ratings were 0.7 and -0.1 for the percentage-correct

(positive) and percentage-incorrect (negative) frames, respec- tively, F(l, 96) = 26.3, p < .0001, r|2 = .54. Numeracy did not have a significant main effect. The interaction of numeracy with

frame, however, was significant, F(l, 96) = 5.6, p < .05, r\ = .11. As hypothesized, less numerate participants showed a stronger framing effect than highly numerate participants1 (see

Fig. 1). This finding is consistent with the highly numerate being

lA numeracy quartile split showed a stronger framing effect among the less numerate. Mean differences between positive and negative frames were 1.3, 0.7, 0.5, and 0.3 for the lowest through highest quartiles, respectively.

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E. Peters et al.

Fig. 1. Numeracy and attribute framing. Error bars represent standard errors of the mean.

more likely to transform numbers from one frame to a different frame.

STUDY 2: NUMERACY AND RISK REPRESENTATION

Dehaene (1997) suggested that although children spend con- siderable time learning the mechanics of math, they may not

really understand how to apply those mechanics even in adult-

hood. We propose, however, that the likelihood of such appli- cation increases with numeracy, so that the highly numerate should find alternative frames of the same number more equally

influential in judgments compared with the less numerate. In

Study 2, we tested this hypothesis using a paradigm developed by Slovic, Monahan, and MacGregor (2000). They conducted studies in which experienced forensic psychologists and psy- chiatrists were asked to judge the likelihood that a mental pa- tient would commit an act of violence. Clinicians told that "20

out of every 100" similar patients would likely commit an act of

violence (a frequency frame) were more likely to refuse to dis-

charge the patient than were clinicians told that the patient had

a "20% chance" of committing an act of violence (a percentage frame).

We hypothesized that highly numerate participants, presented

with a scenario similar to that used by Slovic et al. (2002), would

be more likely than less numerate participants to retrieve the

appropriate numerical principle and transform numbers from one format to another (i.e., 20 out of 100 = 20%). Thus, we expected that the format of presentation would affect judgments

less among the more numerate than among the less numerate.

Fig. 2. Numeracy and percentage (10% of 100) versus frequentistic (10 out of 100) representations of risk. Error bars represent standard errors of the mean.

Method

Participants were 46 volunteers from a psychology course who

read the mental-patient scenario in either a frequency format ("Of every 100 patients similar to Mr. Jones, 10 are estimated

to commit an act of violence to others during the first several

months after discharge") or a percentage format that used the identical wording but substituted "10% are estimated" for "10

are estimated." Using a scale ranging from 1 (low risk) to 6 (high

risk), they rated the level of risk that Mr. Jones would harm

someone. They also responded to the same numeracy and de- mographic items used in Study 1. In addition, they reported their

verbal and quantitative SAT scores, which served as a proxy measure for intelligence.

Results

High-numeracy participants in both conditions and low-nu- meracy participants given the frequency frame rated Mr. Jones

as presenting a medium risk. However, low-numeracy partici- pants given the percentage format rated Mr. Jones as presenting

a significantly lower risk (see Fig. 2); this interaction between

format and numeracy was significant, F(l, 42) = 4.0, p < .05, rf = .42.

Is the numeracy effect due to intelligence rather than nu- meracy per se? Using SAT scores as a proxy for intelligence, we

found that higher SAT scores (verbal and quantitative scores combined) were associated with greater numeracy (r = .26). However, after numeracy scores were regressed onto SAT scores,

the numeracy residuals showed a significant pattern of results

similar to the pattern in Figure 2, specific contrast F(l, 30) = 6.9,/) < .05. We also obtained similar results when we controlled

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Numeracy and Decision Making

only for SAT quantitative scores (the results were somewhat weaker) and when we controlled for SAT verbal scores.

We suspect that high-numeracy participants have relatively equal access to the percentage and frequency formats regardless

of the format in which information is presented to them, whereas

low-numeracy participants consider only the format they are

given. Unpublished follow-up studies by Slovic showed that representations of risk in the form of probabilities (10% of 100

patients) led to relatively benign images of one person, whereas

the "equivalent" frequentistic representations (10 out of 100 patients) created frightening images of violent patients (e.g., "Some guy going crazy and killing someone"). He suggested that

these affect-laden images likely induced greater perceptions of risk in response to the frequency frame, compared with the

probability frame (Slovic, Finucane, Peters, & MacGregor, 2004). Although we did not test this idea directly in the present

study, it is possible that less numerate participants are influ- enced greatly by the affective imagery elicited by the fre- quentistic format and do not have access to this affective imagery when given the percentage format. At the same time,

highly numerate participants may access the affect and affective

imagery regardless of whether they receive information in the

frequency or probability format, so that their risk perceptions

do not vary by format.

STUDY 3: DOES COMPETING AFFECTIVE INFORMATION INFLUENCE THE LESS NUMERATE

MORE THAN THE HIGHLY NUMERATE?

Information in decision making appears to be processed using two different modes of thinking: deliberative and affective-ex-

periential (Epstein, 1994; Loewenstein, Weber, Hsee, & Welch, 2001; Sloman, 1996). How might differences in numerical ability influence how information is processed?

The deliberative mode is conscious, reason based, and rela-

tively slow. In order to deliberate effectively in decisions involving numbers, the individual must have the ability, moti-

vation, and capacity to process numerical information accu- rately even though the logic of "mental arithmetic poses serious

problems for the human brain" (Dehaene, 1997, p. 1 18). When it

comes to deliberating about numbers, the highly numerate clearly have an advantage. The experiential mode of thinking is

primarily affective ; it is automatic, associative, and fast. It is

likely related to gist processing in fuzzy-trace theory (Reyna &

Brainerd, 1991) and may underlie humans' fuzzy and approxi-

mate concept of number (Dehaene, 1997). One of affect's pri- mary functions is to provide meaning and motivation to choice

processes (Damasio, 1994; Peters, in press). We explored the link between numeracy and affect in Studies 3 and 4.

In Study 3, we provided participants with two different rep-

resentations of the same number (frequency and probability) and

tested whether numeracy affected decisions nonetheless. We also began to examine whether numerical ability may influence

the affective meaning of numbers. We measured both affect (the

valence of feelings) and affective precision (the clarity of those

feelings). Past studies have shown affective precision to pre- dict judgments independently of affect (Hsee, 1996; Mellers, Richards, & Birnbaum, 1992).

We used a paradigm developed by Denes-Raj and Epstein (1994), who showed that when offered a chance to win a prize by

drawing a red jelly bean from a bowl, participants often elected

to draw from a bowl containing a greater absolute number, but a

smaller proportion, of red beans (e.g., 9 in 100 or 9%) rather than

from a bowl with fewer red beans but a better probability of

winning (e.g., 1 in 10 or 10%). For these individuals, affective images of 9 winning beans in the large bowl appeared to dom-

inate the image of 1 winning bean in the small bowl. When in-

terviewed, many participants who had made nonoptimal choices

reported a conflict between what they objectively knew were the

better odds and how they felt about the bowl that offered a greater number of winners. A number of subjects indicated that

the larger bowl "looked more inviting."

Affect can be a direct "hit" from an object (similar to Zajonc's,

1980, notion that affect comes before conscious deliberation), or

it can be the result of prior deliberation. We propose that in this

task, affect as a direct hit from the number of winning beans

conflicts with affect from thinking about the stated probability.

We hypothesized that compared with the less numerate, the highly numerate would be more likely to deliberate about and compare probabilities and would draw from this deliberation a

more precise affective reaction that would guide their decisions.

Lacking a clear affective understanding of numbers, the less numerate would rely instead on readily available but less rele- vant affective sources, such as the number of winning beans.

Thus, we predicted that less numerate adults, compared with

highly numerate adults, would draw more often from the larger,

affectively appealing bowl with less favorable objective proba-

bilities. We also expected that affective reactions to the larger bowl, with its smaller probability of winning, would be more

precise and more negative among the highly numerate than among the less numerate.

Method

Participants (N = 46) from Study 2 also completed Study 3 during the same session. They were shown two drawings of bowls

of colored and white jelly beans and told to imagine that they could select 1 bean, and if they selected a colored jelly bean,

they would win $5. The larger bowl, A, contained 100 jelly beans, 9 of which were colored, and was labeled as having "9%

colored jelly beans"; the smaller bowl, B, contained 10 jelly beans, 1 of which was colored, and was labeled as having "10%

colored jelly beans." Participants were asked from which bowl

they would prefer to choose (on a scale that ranged from 6, strong 2Affect is defined as positive and negative feelings about a stimulus (e.g., a

bet).

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E. Peters et al.

preference for A, on the left, to 0 in the middle, to 6, strong

preference for B, on the right); preferences for A were recorded as

negative numbers prior to analysis. Participants were told to imagine that once they chose a bowl, it would be placed behind

a screen, the beans would be mixed, and then they would draw

a bean blindly from their chosen bowl.

After indicating their preference, participants were asked a

question about their affective precision ("How clear a feeling do

you have about the goodness or badness of Bowl A's 9% chance

of winning?"), which they responded to on a scale ranging from

0, completely unclear, to 6, completely clear. Finally, they were

asked about their affect ("How good or bad does Bowl A's 9% chance make you feel?"), indicating their response on a 7-point

scale ranging from -3, very bad, to +3, very good.

Results

Lower numeracy was linked to more suboptimal choices; the less numerate were significantly more likely to choose Bowl A

than were the highly numerate (33% and 5%, respectively), %2(1, N = 46) = 5.2,/) < .05; mean scaled preference was 1.7 for the less numerate and 4.1 for the highly numerate, J(44) = -2.5,

p < .05, d = 0.75. As in Study 2, we controlled for the effect of

our proxy for intelligence. In this analysis, the less numerate were still more likely to make an objectively worse choice than

the highly numerate (the difference was significant when con-

trolling for SAT verbal scores and was marginally significant when controlling for overall or quantitative SAT scores).

Analysis of the affect variables revealed that numeracy was not significantly associated with affect about Bowl A's 9% chance (mean affect = -0.5 and -1.1 for low- and high-nu- meracy participants, respectively,/) = .13, d = .46). However, the less numerate had less precise feelings about the 9% chance

than the highly numerate did (affective precision = 3.7 and 5.0,

respectively), *(44) = -2.6,/) < .01, d = 0.78.

STUDY 4: DO THE HIGHLY NUMERATE AND LESS NUMERATE RETRIEVE DIFFERENT AFFECT FROM PROBABILITIES AND NUMERICAL COMPARISONS?

In this study, we examined whether the highly numerate may

sometimes make less "rational" responses than the less nu- merate precisely because they focus on the detail of numbers

and draw more affective meaning from numerical comparisons.

We used a paradigm (reported in Slovic et al., 2004) in which one

group of subjects rates the attractiveness of a simple gamble (7

chances out of 36 to win $9; otherwise, win $0) on a scale from 0

through 20; a second group uses the same scale to rate a similar

gamble with a small loss (7 chances out of 36 to win $9; 29 chances out of 36 to lose 50 ). With this paradigm, Slovic et al.

obtained data that were anomalous from the perspective of economic theory. The mean rating of the first gamble was 9.4.

When the possible loss of 50 was added to the gamble, the mean

attractiveness jumped to 14.9, and there was almost no overlap between the distributions of responses for the two groups.

We hypothesize that these curious findings can be explained by affect and affective precision. According to this view, a probability maps relatively precisely onto the attractiveness scale, because it has an upper and lower bound and people know

where a given value falls within that range. The highly numerate,

who are expected to deliberate more about numbers than the less

numerate, should draw a more precise affective reaction from

probability's boundedness. In contrast, the mapping of a dollar

outcome (e.g., $9) onto the scale is less precise, reflecting a failure to know whether $9 is good or bad, attractive or unat-

tractive. Thus, the impression of the gamble offering a win of $9

and no losing payoff is dominated by the rather unattractive

impression produced by the 7/36 probability of winning. How-

ever, adding a very small loss to the payoff dimension puts the $9

payoff in perspective (i.e., it makes the payoff more affectively

precise to the subject) and gives it meaning. The combination of

a possible $9 gain and a possible 50 loss has a very attractive win/lose ratio, leading to a relatively precise mapping onto the

upper part of the attractiveness scale. Whereas the imprecise mapping of the $9 when it is not combined with a loss carries

little weight, the more precise and favorable impression of the $9

in the context of the small loss carries more weight, thus leading

to an increase in the overall favorability of the gamble. We reasoned, however, that the ease of mapping results from the $9:

-50 bet creating a perception of upper and lower bounds similar to probability's boundedness and similar to comparing the 9% and 10% probabilities in Study 3. On the basis of the results in Study 3, we hypothesized that the highly numerate would draw more affective meaning from the $9:- 50 compar- ison than the less numerate would, and thus would show a

greater difference in their ratings of the two bets.

Method

Participants were 171 volunteers from a psychology depart- ment's subject pool (54% female; mean age = 19). In a between-

subjects design, participants were asked to rate their opinion about the attractiveness of playing a bet, using a 21 -point scale

ranging from 0, not at all an attractive bet, to 20, extremely at-

tractive bet. Half of the participants responded to a bet that consisted of "7/36 chances to win $9 and 29/36 chances to win

nothing" (the no-loss bet), and the other half of the participants

responded to the bet "7/36 chances to win $9 and 29/36 chances

to lose 50" (the loss bet). Participants were then asked to rate their affect and affective precision toward both the $9 win and

the 7/36 chance of winning, using the same scales described in

Study 3. They reported SAT verbal and quantitative scores and completed the numeracy scale and demographic items last.

Results

Participants high in numeracy rated the objectively better no-

loss bet as less attractive than the loss bet, t(S9) = 3.1,/) < .01

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Numeracy and Decision Making

Fig. 3. Numeracy and rated attractiveness of a bet with and without a small loss. Error bars represent standard errors of the mean.

(see Fig. 3), whereas those lower in numeracy rated the two bets

the same on average. A regression using the attractiveness rating

as the dependent variable and bet condition (coded as no loss = 0 and loss = 1), numeracy (0 = low and 1 = high), and their interaction as independent variables revealed only a significant

interaction, t(l) = 2.2,/) < .05, d = 0.34. The analysis control- ling for SAT scores showed that the highly numerate who respond- ed to the loss bet rated their bet as more attractive than did the

other three groups, specific contrast F(l, 151) = 9.1,/? < .01. The highly numerate had less negative feelings about the 7/36

chances of winning than the less numerate did (mean affect =

0.0 and -0.6, respectively), *(169) = 2.7, p < .01, d = 0.44. They also reported more clear feelings about the 7/36 chances of

winning (mean affective precision = 4.5 and 3.9, respectively),

*(149) = 2.4,/) < .05, d = 0.38. The highly numerate had more positive affect toward the $9 win in the loss condition than in the

no-loss condition, whereas the less numerate showed no sig- nificant differences in affect between the conditions, mean af-

fect = 1.9 and 1.3 for the highly numerate in the loss and no-loss

conditions, t(S9) = 2.3,/) < .05, d = 0.47, and mean affect =1.0 and 1.3 for the less numerate in the same conditions, n.s. Af-

fective precision to the $9 showed no significant differences.

In summary, the highly numerate found the loss bet more at-

tractive than the no-loss bet; participants lower in numeracy rated the loss and no-loss bets as equally attractive. These findings suggest that the highly numerate may sometimes make

worse decisions than the less numerate (although it could be argued that the small loss allowed only the highly numerate to

recognize the goodness of this positive expected-value bet). The

difference between the groups was linked with different feelings

that they derived from the numbers. The highly numerate had

more clear and less negative affect toward the 7/36 chances of

winning. In addition, they had greater positive affect toward the

$9, particularly in the loss condition.

These results are consistent with our hypothesis that com- pared with the less numerate, the highly numerate tend to derive

more affective meaning (generally stronger or more precise af-

fective meaning) from probabilities and numerical comparisons. We were also interested, however, in whether these affective

differences mediated the impact of numeracy on the attrac- tiveness ratings. To do this, we examined whether ratings of affect toward the 7/36 chance of winning mediated any main

effect of numeracy on attractiveness ratings. First, a regression

of the attractiveness scores indicated a significant main effect of

numeracy on attractiveness, F(l, 169) = 8.0,/) < .01. Second, in a regression of affect toward the 7/36 chances of winning, high-

numeracy participants had less negative affect toward the 7/36

chances than those who were less numerate, F(l, 169) = 7.2, p < .01. A final regression of attractiveness ratings included affect to the 7/36 chances and numeracy as independent vari-

ables. Consistent with the hypothesized mediation, the influence

of numeracy on attractiveness was no longer significant, but participants with greater positive affect toward the 7/36 chance

rated the bet as more attractive, b = 1.4, t(l) = 5.3,/) < .001; Sobel z = 2.4, p < .05. Precision of affect toward the 7/36 chance did not demonstrate mediation.

Finally, we tested whether ratings of affect toward the $9 win

mediated the effect of high numeracy on the differential at- tractiveness of the loss and no-loss bets. We first demonstrated

that high-numeracy participants in the loss condition rated their

affect toward the $9 win as more positive than other participants

did, F(l, 169) = 8.5, p < .01. A second regression showed that both the numeracy-by-condition interaction and affect toward

the $9 were significant predictors of attractiveness ratings. Af-

fect toward the $9 appeared to partially mediate the relation hetween the numeracy-by-condition interaction and attractive-

ness ratings, Sobel z = 1.7, p < .10. There was no evidence that affective precision toward the $9 mediated attractiveness rat-

ings.

GENERAL DISCUSSION

A series of four studies explored how the ability to understand

and transform probability numbers relates to performance on

judgment and decision tasks. Each task involved the processing of numbers; some tasks involved the processing of affect from the

numbers themselves or from a competing source. Findings from

Studies 1 and 2 were consistent with our hypothesis that com-

pared with low-numeracy adults, high-numeracy adults are more likely to retrieve and use appropriate numerical principles

and transform numbers presented in one frame to a different

frame. We believe that low-numeracy decision makers are left

with information that is less complete and less understood, lacking in the complexity and richness available to the more numerate. Results from Studies 3 and 4 were consistent with our

hypothesis that the highly numerate tend to draw more affective

meaning from probabilities and numerical comparisons than the

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E. Peters et al.

less numerate do. Study 3 demonstrated that the less numerate

were more influenced by an irrelevant affective source, perhaps

because they drew less precise affective meaning from relevant

numbers. In Study 4, the influence of numeracy on the attrac-

tiveness of the bet was partially mediated by affect. The alter-

native hypothesis that numeracy's effect on decisions is due to

general intelligence was not supported by these studies.

The present research is an initial attempt to examine the roles

of numeracy and affect in decision making. We examined the extent to which numerical ability serves as a mediator of deci-

sion performance (helping performance in some situations and

hurting performance in others). Our measure of numeracy re-

quires further development, but demonstrated fairly strong re- lations with decisions nonetheless. We also examined whether

numeracy influences affect and affective precision and found

that affect partially mediates the influence of numeracy in some

decisions. This research adds to the growing body of knowledge

concerning how affective and deliberative ways of thinking may

influence important effects in decision making. It also demon-

strates that individuals may differ in the type of assistance they

need in making decisions. Those low in numerical ability may need different decision aids than those high in numerical ability.

Acknowledgments - We thank Yuval Rottenstreich, Isaac Iipkus,

Robert Mauro, and Barbara Fasolo. This work was supported by

the National Science Foundation (0339204).

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(Received 4/15/05; Accepted 7/14/05; Final materials received 8/3/05)

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